reviews: 
Comments: This paper proposes a new approach for learning dynamics from the observation of distributions at different time steps. The paper proposes to use an unbalanced optimal transport approach that allows modeling particle growth or death over time, which is an important aspect of single cell dynamics modeling. The authors compare their approach on datasets from syntethic gene regulatory networks and single cell trajectories dynamics. The paper shows favorable performance results compared to previous methods.
Strengths: - Population dynamics from snapshot data is an important problem, especially in biological application such as single cell trajectories inference.
- The proposed method appears to surpass the performance of previous methods.
- The related works section is extensive.
Weaknesses: - One of the most important weaknesses of this paper at this stage is its clarity. In its current form, the paper is poorly written, and the ideas are poorly motivated. The main limitation from prior works identified is the unabalanced aspect e.g. "However, computational methods for learning high-dimensional unbalanced stochastic dynamics from snapshots without prior knowledge of growth and death or additional information are still lacking.". Yet, the paper only indirectly addresses that issue, which confuses the reader. Despite the favorable experimental results, the current presentation of this paper prevents it from being appreciated by the community.

- Section 5, which is the core of your method, is extremly confusing. For instance, the reconstruction loss is not introduced previously such that it's extremely challenging to follow the development until the final loss in Equation 10. The algorithm 1 does not provide any help either in much needed clarification. The algorithm is too laconic and does not refer to corresponding parts of the text.

- It's not clear to me why the connection with the Schrodinger bridge is necessary. As far as my reading goes, it seems that you only need to leverage the dynamic version of regularized unbalanced OT. As such, it does not seem that the connection with Schrodinger bridges helps the reader understand the method, and you don't leverage that connection later on in your method.

- Theorem 4.1 uses $v$ which is not introduced previously. It's later undertstood that it corrresponds to the vector field of the corresponding ODE but this hinders the clarity of the paper.

- The presentation of the results in Figure 2 raises questions. Why does panel (b), with the true dynamics has ground truth, predicted and trajectories, if it is the ground truth dynamics ? What is the "predicted" in this case ? 

- Because the most important contribution of this paper relies on modeling the growth rate, an ablation study is required where the growth rate part of the method is disabled (e.g. g = 0). This would allow to understand the impact of it on the final performance. 

- Despite the extensive related works section, the experiments only compare with two baselines. Baselines such as Bunne et al. or Yutong et al. could also be considered.

Sha, Yutong, et al. "Reconstructing growth and dynamic trajectories from single-cell transcriptomics data."
Recommendation: 8
Reviewer confidence: 3
Soundness/correctness: 3
Clarity: 3